GATE Data Science and Artificial Intelligence 2024 | Sample Paper | Question: 16

Question

Which of the following statements is/are TRUE?

• A. Every relation with two attributes is also in $\mathrm{BCNF}$.
• B. Every relation in $\mathrm{BCNF}$ is also in $3 \mathrm{NF}$.
• C. No relation can be in both $\mathrm{BCNF}$ and $3 \mathrm{NF}$.
• D. None of Above

Answer 1

A)Every relation with two attributes is also in BCNF.

TRUE.
BCNF states that give X->Y, X should be a key
Given 2 attributes A and B, if there are Functional dependencies, since if A→B is a valid FD, then A is a key in the given relation. Similar argument follows for other possible FDs in a 2 attribute relation.

B) Every relation in BCNF is also in 3NF

TRUE- by the definition of BCNF

C) No relation can be both in BCNF and 3NF

FALSE. Since BCNF implies 3NF

D) None of Above.
FALSE. since A and B are true

ANSWER
A & B

Answer 2

1 every relation with two attribute violate the 1NF , so it cant be BCNF

2 every relationship is BCNF means its satisfy all others 1NF , 2NF and 3NF , so its CORRECT

3 thats not correct , it depends upon relations 

4 this is already false 

Answer 3

(B) Every relation with two attributes is in BCNF.  (A) Every relation in BCNF is also in 3NF.

This statement is TRUE. For relations with two attributes, achieving BCNF is straightforward, and they will inherently satisfy the BCNF condition.

Why the other options are incorrect:

• (C) No relation can be in both BCNF and 3NF: This is false, as explained above. A relation in BCNF is also in 3NF by definition.
• (D) Every relation in 3NF is also in BCNF: This is not true. There are relations that can be in 3NF but not BCNF, as BCNF has additional restrictions.